HOMEWORK ASSIGNMENT #3

ME 303 FLUID DYNAMICS/ WESTPHAL/ WSU/ FALL 2000

• Follow the Homework Guidelines for preparing your submission.
• You are encouraged to work together with other students, but the work you submit cannot be a machine-produced duplication of another student's work - it must be an original, but can represent your version of a collaborative effort.
• Late work not accepted!
• Careful use of control volume analysis is crucial to success for the problems below involving application of conservation of mass!
• Identification of streamlines is crucial when applying the Euler "S" and/or "N" equations (Euler "S" is aka "Bernoulli" or "Field" equation)

The assignment consists of the problems given below.

1. Calculate the discharge (volumetric flowrate) and mass flowrates for the cases below. Omit discussion.
   • A 15 ft/s air flow (100 kPa abs and 20 deg C) in a 2 ft by 3 ft building air conditioning system (results in cfm and lbm/min);
   • water flow at 8 ft/s in a 3/4 inch pipe (result in gpm and lbm/hr);
   • water flowing at 5 ft/s in a riverbed 1000 ft wide and 25 ft average depth (result in cfs and lbm/sec).
   
   
2. A high-efficiency ("HEPA"-type) filter is to be specified for a building air handling system that carries 20,000 cfm (cubic feet per minute) actual volume flowrate at 100 kPa absolute static pressure and 25 deg C. Such filters are typically limited to a maximum "face velocity" of about 250 fpm (feet per minute). What mass flowrate corresponds to this volume flow? What minimum filter area would be required? Omit discussion.
   
   
3. Answer the following questions related to a 2 m diameter, 4 m tall, cylindrical vat. No discussion beyond answering the questions posed is requested.
   • What is the tank volume?
   • How long would it take to fill the initially empty vat with a liquid volumetric flowrate of 200 gpm into the vat and no outflow?
   • If the tank was initially full, how long would it take to drain the tank through a 5 cm diameter hole in its bottom, if the flow velocity of fluid leaving is (2*g*h)^1/2, where h is the depth of fluid above the hole? NOTE: The general problem of gravity draining of a tank of liquid is a classic one, and is called "Toricelli's problem" after the 17th century Italian who first solved it.
   • Suppose the 5 cm diameter hole in the bottom was open, and the tank initially empty, when an inflow of 200 gpm was initiated. Find the equilibrium tank depth, and, for your discussion, describe how the tank depth would vary with time--you should include a sketch of depth vs. time.
   
   
4. text, problem 4.62; omit discussion. HINT: Your cv should MOVE WITH THE FALLING CYLINDER.
   
   
5. text, problem 4.63; omit discussion. NOTE: This problem is not quite as simple as it might first appear... remember to use V_in,rel!!
   
   
6. text, problem 4.93 DISCUSSION: What would be the effect of increasing the exit gas temperature to 2500 C?
   
   
7. A piston and vertical cylinder contain an open, 3 foot deep column of water at 40 deg. C.
   • What would be the pressure at the piston face if the piston is accelerated upward at 20 ft/s²?
   • Determine the downward acceleration of the piston that would create cavitation within the water.
   
   
   
8. The 30 inch diameter tub of a washing machine spins about a vertical axis at 150 rpm. Sketch the shape of the free surface of the water in the tub assuming that the water moves in solid body rotation (no relative motion, so no shear stresses), and determine the difference in water free surface elevation between the center and the outside of the tub. Omit discussion.
   
   
9. Using Euler's "N" equation (F=ma normal to a streamline) and assuming ideal and uniform flow, estimate the pressure difference between the inner and outer walls of a tight (inner radius equal diameter) 1 ft diameter pipe bend with a water flowrate of 15 cfs (cubic feet per second). For your discussion: explain how this phenomena could be incorporated into an approach to flow metering. Could the pressure difference be measured with a manometer?
   
   
10. A 50 m/s jet of water issues from the 20 mm nozzle of a firehose. The hose diameter upstream of the nozzle is 60 mm.
    • What is the discharge?
    • Calculate the pressure in the hose upstream of the nozzle assuming ideal flow.
    • Determine the stagnation pressure of the exiting jet. For your discussion, explain why the exit stagnation pressure is not equal to the (static) pressure in the hose upstream of the nozzle.